Apparatus and methods for measurement system calibration

ABSTRACT

Apparatus and methods for calibrating a transducer measurement system having a plurality of subsystems, permitting total system calibration by a few selected adjustments without requiring complete system calibration when a new subsystem is added or a subsystem replaced and without requiring adjustments to be made to each individual subsystem. The measurement system provides a calibrated measurement signal indicative of a characteristic of an object with which the transducer interfaces. Each subsystem is characterized in terms of a minimum number of parameters associated therewith and the parameters are mathematically combined to reflect values of adjustable subsystem or system components. In this manner, variations associated with each separable subsystem from nominal, specified values, are combined and corrected by a single adjustment of a minimum number of selected adjustable components representing the degrees of freedom for errors in the system. In an alternate embodiment, a signal processor is responsive to the subsystem describing parameters for processing a digital replica of a measured signal to provide the calibrated measurement signal.

This application is a division of application Ser. No. 08/052,384, filedApr. 23, 1993.

FIELD OF THE INVENTION

This invention relates generally to measurement systems and moreparticularly, to transducer measurement system apparatus and methods forimproved calibration.

BACKGROUND OF THE INVENTION

Transducer measurement systems are known for measuring variouscharacteristics of an object, such as temperature, thickness,conductivity, etc. In one such system, the transducer provides an outputsignal that is processed to generate an electrical signal having avoltage level related to the distance between the transducer and theobject. In one exemplary use of the system, the transducer is acapacitive probe and the characteristic of the object to be measured isthe flatness of the object. Such a measurement is provided by obtainingmultiple transducer output signals in response to measurements atmultiple locations of a particular object. Examples of typical objectsare semiconductor wafers and disks for disk drives.

As is known, such measurement systems generally include a plurality ofsubsystems, such as inter alia, a transducer subassembly, a "front end"circuit, such as may contain a preamplifier, for converting thetransducer output signal into a corresponding electrical signal having avoltage level related to, and ideally proportional to, the measuredcharacteristic, a signal conditioning circuit for conditioning theelectrical signal and providing an output measurement signal indicativeof the measured object characteristic, and a display circuit fordisplaying a representation of the measured object characteristic.Ideally, parameters of the constituent subsystems meet predeterminedspecifications so that the output measurement signal has a knownmathematical relationship to the measured object characteristic.However, typically these parameters vary within a range due to sucheffects as component tolerances and stray capacitance. When thesubsystem parameters vary, the output measurement signal may not be anaccurate representation of the measured object characteristic, but maybe in error in such parameters as gain, offset, linearity, etc.

One technique used for calibrating transducer measurement systems inorder to ensure that the output measurement signal maintains a knownrelationship to the measured characteristic is to perform a "systemlevel calibration" using one or more reference objects (i.e., an objecthaving a known characteristic to be measured). More particularly, outputsignals from the integrated system, obtained in response to severalreference objects, are set to predetermined reference levels byadjusting one or more variable components within the system. That is,the variable component is adjusted until the output signal is broughtinto conformity with predetermined values. For example, an adjustmentmay be achieved by adjusting a potentiometer within the system. Withthis calibration technique, if one of the subsystems is replaced, thesystem level calibration must be repeated. Thus, obtaining a replacementsubsystem requires the user to either send the entire measurement systemback to the manufacturer for subsystem replacement and systemre-calibration, have a repair person travel to their facility to replacethe subsystem and re-calibrate the system, or possess the requisiteskill and apparatus for re-calibrating the system after installation ofa replacement subsystem.

Another technique for calibrating transducer measurement systems is a toperform a "subsystem level calibration" in which each individualsubsystem is calibrated separately. More particularly, the output signalfrom a subsystem, obtained in response to each reference object, is setto a predetermined value for that subsystem by adjusting variablecomponents within that subsystem. Each subsystem is adjusted, until thefinal output signal is brought into conformity. However, this type of"subsystem level calibration" tends to be labor intensive sinceadjustments must be made to each individual subsystem.

SUMMARY OF THE INVENTION

In accordance with the present invention, apparatus and methods areprovided for calibrating a transducer measurement system having aplurality of subsystems in a manner that avoids calibration of theentire system when a new subsystem is added or when a subsystem thereofis replaced and also that avoids adjusting each individual subsystem,while maintaining accurate calibration or acceptably close to thatstandard. The transducer measurement system provides a calibratedmeasurement signal indicative of a characteristic of an object withwhich the transducer interfaces. Preferably, each subsystem is initiallycharacterized to determine at least one parameter associated with italone which is descriptive of variations associated with that subsystemfrom a nominal, specified value. Such parameter may represent variationsof the subsystem due to the effects of component tolerances or straycapacitance which, if not compensated, may result in errors in themeasured signal. The set of such subsystem describing, or variationindicating, parameters is converted, mathematically, into adjustments ina minimum number of adjustable components located in the system atselected points so that, when thus adjusted, the total system outputwill be in conformity with a predetermined standard even thoughindividual subsystem outputs may deviate from a nominal, predeterminedvalue. In an alternate embodiment, a signal processor is responsive tothe set of subsystem describing parameters for processing a digitalreplica of a measured signal to provide a digital calibrated measurementsignal.

With both such arrangements, a benefit over subsystem level calibrationis achieved in that the number of actual circuit adjustments may beminimized (i.e., as compared to adjusting each individual subsystem asis done in conventional subsystem level calibration). However, thepresent calibration apparatus and techniques do not suffer the drawbackassociated with conventional system level calibration by requiring"re-calibration" of the entire system whenever a subsystem is added orreplaced. When a subsystem of the present invention is added orreplaced, its descriptive characteristics or parameters, determinedbefore installation, are used in the mathematical algorithm incombination with the characterized parameters of the remaining,unreplaced subsystems, to determine a new set of adjustments. When suchadjustments are made, the system as a whole will then perform with thesame accuracy as if a complete system calibration had occurred, oracceptably close to that standard.

More particularly, in one embodiment, a measurement system includes atransducer, having at least one transducer parameter associatedtherewith, which interfaces with an object to provide a transduceroutput signal. A signal conversion and conditioning circuit, coupled tothe transducer, converts the transducer output signal into anintermediate signal having a voltage amplitude related to the measuredobject characteristic. The signal conversion and conditioning circuit isadjustable in accordance with a mathematical combination of at least oneof the transducer parameter and the signal conversion and conditioningparameter to provide a calibrated measurement signal indicative of themeasured object characteristic.

Exemplary parameters describing the transducer subsystem, which in oneembodiment is a capacitive probe, are a transducer gain parameter and atransducer stray capacitance parameter. The signal conversion andconditioning circuit may also be described by corresponding gain andstray capacitance parameters. The signal conversion and conditioningcircuit includes an adjustable component, such as a set of switchesestablishing a digital word, the value of which adjusts the digitalinput signal of a digital to analog converter, with the switches beingpositioned in accordance with the mathematically determined adjustments.In one embodiment, the signal conversion and conditioning circuitincludes a plurality of adjustable components, each one corresponding toa degree of freedom of error of the measurement system to provide thecalibrated measurement signal. For example, a first adjustable componentcorresponds to the gain error of the entire system and a secondadjustable component corresponds to the linearity error of the entiresystem.

In accordance with an alternate embodiment of the invention, ameasurement system for measuring an object characteristic, includes atransducer having at least one variation indicating parameter associatedtherewith and interfacing with the object to provide a transducer outputsignal. A signal conversion and conditioning circuit, coupled to thetransducer and having at least one variation indicating parameterassociated therewith, converts the transducer output signal into anintermediate signal having a voltage amplitude related to the measuredobject characteristic and provides a digital replica signalcorresponding to the intermediate signal. A signal processor processesthe digital replica signal in response to a mathematical combination ofat least one of the transducer parameter and the signal conversion andconditioning parameter to provide a digital calibrated measurementsignal indicative of the measured object characteristic.

BRIEF DESCRIPTION OF THE DRAWINGS

The foregoing features of this invention, as well as the inventionitself, may be more fully understood from the following detaileddescription of the drawings in which:

FIG. 1 is a block diagram of a calibrated transducer measurement systemin accordance with one embodiment of the invention;

FIG. 2 is a circuit schematic of an embodiment of the transducermeasurement system of FIG. 1;

FIG. 3 is a block diagram of a calibrated transducer measurement systemhaving a signal processor in accordance with an alternate embodiment ofthe present invention; and

FIG. 4 is a detailed block diagram of an embodiment of the transducermeasurement system of FIG. 3.

DESCRIPTION OF THE PREFERRED EMBODIMENT

Referring to FIG. 1, a generalized transducer measurement system,including a measuring circuit 14 and a post-processing circuit 16, isprovided to measure a characteristic of an object 12. The measuringcircuit 14 includes a transducer 20 adapted for interfacing with theobject 12 to measure a desired characteristic thereof, such as flatness,temperature, conductivity, etc. More generally however, the object 12 isan entity having a physical characteristic to be measured. Moreover, thetransducer 20 is an appropriate device for measuring the desiredcharacteristic of a particular object and may, for example, be acapacitive probe or a strain gauge. The measuring circuit 14 furtherincludes a signal conversion and conditioning circuit 22, coupled to thetransducer 20, and here, shown to include a front end circuit 22a and asignal conditioning circuit 22b. More particularly, the transducer 20provides a transducer output signal P(x, a, b), or signal 27, to thefront end circuit 22a which converts the transducer output signal 27into an intermediate signal F(P, c, d), or signal 29, having a voltageamplitude related to the measured object characteristic. Stateddifferently, the front end circuit 22a provides an excitation to thetransducer 20 and recovers an electrical signal therefrom related to themeasured characteristic. For example, when the measured objectcharacteristic is distance or displacement, transducer 20 may be acapacitive probe, used to provide a transducer output signal 27indicative of the capacitance measured between the transducer 20 and theobject 12, and front end circuit 22a converts the capacitance indicatingtransducer output signal 27 into an intermediate electrical 29 signalhaving an amplitude related to the distance between the transducer 20and object 12. Moreover, a plurality of such distance measurements maybe taken at a corresponding plurality of locations of an object toobtain a measure of the flatness of the object.

The signal conditioning circuit 22b receives and processes theintermediate signal 29 to provide a calibrated measurement signal O(F,g, h), or signal 32, indicative of the measured object characteristic.The signal conditioning circuit 22b may comprise analog filteringcircuits, for example. Post-processing circuit 16 receives the analogcalibrated measurement signal 32 and displays a representation thereofto a user. While the generalized transducer measurement system of FIG. 1is shown to include a transducer subsystem 20, a front end subsystem22a, and a signal conditioning subsystem 22b, it is noted that othersubsystem arrangements are suitable for calibration in accordance withthe present invention.

The transducer 20 has at least one parameter, and here two parameters a,b, associated therewith which describe the subsystem 20. Moreparticularly, each such subsystem describing parameters a, b isindicative of a variation of the subsystem from a nominal predetermined,or specified, value and thus, may be alternatively referred to asvariation indicating parameters a, b. Such variations may be caused bycomponent tolerances or other phenomena such as stray capacitance which,if not compensated by calibration, may result in errors in the measuredsignal.

The variation indicating parameters a, b of the transducer subsystem 20are determined, or characterized, and used to calibrate the measurementsystem of FIG. 1 in a manner described hereinafter. In one embodiment inwhich the transducer 20 is a capacitive probe, the transducer outputsignal 27 may be expressed by: ##EQU1## where A_(p) is a gain parameterof the transducer 20, ε_(O) is a constant, here equal to 8.850×10⁻¹²farads/meter, x is the measurement variable (which in the above exampleis the distance between the transducer 20 and the object 12), and Co₁ isa stray capacitance parameter associated with the transducer 20. Thetransducer gain A_(p) and the transducer stray capacitance Co₁ areparameters associated with the transducer 20 which describe variationstherein from a nominal, specified value so that here, variationindicating parameter a=A_(p) and b=Co₁ as indicated in equation (1)above. Similarly, the signal conversion and conditioning circuit 22 and,more particularly, the front end circuit 22a thereof, has at least oneparameter, and here two parameters c, d, associated therewith which aredescriptive of such subsystem, such parameters c, d also beingdetermined, or characterized, and used to calibrate the measurementsystem of FIG. 1. The intermediate signal 29 may be expressed generallyby: ##EQU2## where V_(d) is a front end drive signal and C_(r) is areference capacitor value, both of which will become apparent from thediscussion of FIG. 2 below. A gain parameter associated with the frontend circuit 22a is given by A_(s) and Co₂ is a stray capacitanceparameter associated with the front end circuit 22a. The front end gainA_(s) and the front end stray capacitance Co₂ describe variations of thefront end circuit 22a from nominal, predetermined values so that here,subsystem describing parameter c=A_(s) and d=Co₂, as indicated inequation (2) above.

The generalized system of FIG. 1 includes a minimum number of adjustablecomponents for eliminating the variations associated with all of theconstituent subsystems thereof from corresponding predetermined values.Here, the signal conversion and conditioning circuit 22 includesadjustable components 30a, 30b which are adjustable in response tovariation indicating parameters a, b, c, and d. That is, the system canbe truncated here, or the signal conditioning 22b, having variationindicating parameters g and h associated therewith, may be included toprovide adjustments for components 30a, 30b. The signal conversion andconditioning circuit 22 is adjustable in accordance with adjustmentsdetermined by a mathematical combination of at least one of thevariation indicating parameters a-b, c-d, and g-h, and as many as allsuch parameters, as represented generally by the following formula:##EQU3##

In ideal operation, the parameters (i.e., a-b, c-d, and g-h) associatedwith each of the subsystems (i.e., transducer 20, front end circuit 22a,and signal conditioning circuit 22b, respectively) have nominal,specified values, so that when such subsystems are interconnected toprovide measurement system of FIG. 1, the resulting measurement signalis an accurate representation of the measured object characteristic.Stated differently, preferably each of the subsystems 20, 22a, 22b has aknown, specified transfer function so that in response to a referencemeasurement, the resulting measurement signal conforms to apredetermined value. However typically phenomena, such as straycapacitance and component tolerances, cause an error in the outputmeasurement signal.

The present invention reduces, and preferably removes, any such error inthe output measurement signal by providing calibration with a minimumnumber of adjustable components at selected system locations. Asmentioned, the signal conversion and conditioning circuit 22 isadjustable in accordance with adjustments determined by mathematicallycombining the subsystem describing parameters of each individualsubsystem, in accordance with equation (1) above. The resultingadjustments S₁, S₂ represent a particular setting of adjustablecomponents 30a, 30b. In this way, error, otherwise present in theresulting measurement signal, is compensated. Put a different way, thetransfer function of the circuit 22 (i.e., the relationship between themeasurement output signal 32 and the transducer output signal 27) isadjusted in response to adjustments S₁, S₂ to provide the calibrationmeasurement signal 32, accurately representing the measuredcharacteristic of object 12.

In this way, each subsystem 20, 22a, 22b is characterized by one or moreparameters a-b, c-d, g-h associated therewith, respectively, that fullydescribe the variations thereof from nominal, predetermined values.Moreover, these variation indicating parameters a-b, c-d, g-h aremathematically combined to reflect a preferably minimum number ofadjustment values S₁, S₂ of adjustable components 30a, 30b,respectively. More generally, the number n of adjustments S₁, S₂ (i.e.,here n=2) is preferably less than the number x of subsystem describingparameters a, b, c, d, g, and h (i.e., here x=6). In this manner,variations associated with each separable subsystem 20, 22a, 22b arecombined and corrected by a single adjustment of a minimum number ofselected, adjustable components 30a, 30b. Note however that the numberof parameters required to describe a particular subsystem, as well asthe number and arrangement of adjustable components 30a, 30b may bevaried. For example, adjustments S₁, S₂ may be matrices of more than oneparameter or dimension. In the illustrative embodiment described belowin conjunction with FIG. 2, the system is truncated in that adjustmentsS₁, S₂ are provided by mathematically combining parameters a-d, withoutadditional parameters g, h. Put a different way, the front end circuit22a and the signal conditioning circuit 22b jointly have two parametersc, d associated therewith, as will be described.

The procedure for determining the parameters of the transducer subsystem20 and the signal conversion and conditioning subsystems 22a, 22b may bereferred to as "virtual subsystem characterization" and will bedescribed in detail below in conjunction with FIG. 2. Suffice it here tosay however that subsystem characterization generally refers to a methodby which each of the subsystem parameters is measured, or otherwisedetermined. "Virtual", in conjunction with the characterization employedherein, indicates that the determined parameter information for aparticular subsystem is not necessarily used in that subsystem to adjustthat individual subsystem to a normalized, or variation freeperformance. Rather, such parameters are mathematically combined inaccordance with equation (3) and used to adjust a selected, minimumnumber of adjustable component or components 30a, 30b within thegeneralized system of FIG. 1.

With this arrangement, an advantage over conventional subsystem levelcalibration is achieved in that the number of actual circuit adjustmentsmay be minimized (i.e., as compared to adjusting each individualsubsystem). That is, whereas conventional subsystem level calibrationinvolves adjusting components within each subsystem in response toreference measurements, the present apparatus and method contemplatesconverting the set of variation indicating parameters from eachsubsystem into an adjustment for adjusting a minimum number ofcomponents located in the system at selected points so that, when thusadjusted, the system output signal 32 is calibrated, or brought intoconformity with a specified standard, even though individual subsystemoutputs may vary from a nominal, specified value. In this way, the timeand labor required to calibrate the measurement system are reduced ascompared to conventional subsystem level calibration.

Moreover, the present calibration apparatus and techniques do not sufferthe drawback associated with conventional system level calibration byrequiring "re-calibration" whenever a subsystem is added or replaced.When a subsystem of the present system is replaced, calibration isachieved by using the subsystem describing parameters associated withthe replacement subsystem in the mathematical algorithm of equation (3),in combination with the parameters of the remaining, unreplacedsubsystems, to determine a new set of adjustments. In this way,replacement and servicing of the transducer measurement system issimplified as compared to conventional system level calibration, therebyreducing the associated cost and potential down-time of the measurementsystem.

Referring now to FIG. 2, an illustrative embodiment of the system ofFIG. 1 is shown to include two adjustable components 31a, 31b adjustedin accordance with adjustments S₁, S₂ as noted above. The transducer 20is coupled in the feedback path of an operational amplifier 40, in amanner similar to that described in U.S. Pat. No. 4,918,376, issued onApr. 17, 1990, assigned to the assignee of the present invention, andincorporated herein by reference. More particularly, the signalconditioning circuit 22b includes an AC drive signal source 42 providingan AC drive signal V_(d) (related, or corresponding, to a nominal drivevoltage setting V_(d) ') to an input terminal 44a of a gain adjusting,multiplying digital to analog converter (DAC) 44, the output terminal44c of which is coupled via line 45 to the inverting input of anoperational amplifier 46 through a resistor R2. The signal conditioningcircuit 22b further includes signal conditioning circuitry such an asanalog filter, filtering the intermediate signal 29 to provide thecalibrated measurement signal 32. Resistor R4 is coupled in the feedbackpath of operational amplifier 46 and, in conjunction with resistor R2and gain DAC 44, adjusts the gain of the measuring circuit 14. Moreparticularly, a control terminal 44b of the gain DAC 44 is coupled to adigital word generator 31b that expresses the value S₂ to adjust thevoltage at the output terminal 44c thereof. Digital word generator 31bmay, for example, include a plurality of switches positioned to providea ten bit digital input to DAC 44 in accordance with adjustmentexpression S₂ and in response to which the drive voltage V_(d) ismultiplied by a predetermined scale factor. In this way, the gainassociated with the drive signal and thus, the transfer function of thesignal conversion and conditioning circuit 22, is concomitantlyadjusted.

The non-inverting input of operational amplifier 46 is coupled to thenon-inverting input of an operational amplifier 40 through a resistorR6, as shown. Also coupled between the non-inverting inputs ofoperational amplifiers 40, 46 is the series combination of a resistor R8and a second multiplying digital to analog converter (DAC) 50, referredto herein as linearity DAC 50. A resistor R10 is coupled between thenon-inverting input of operational amplifier 46 and ground and theoutput of operational amplifier 46 is coupled to the inverting input ofoperational amplifier 40 through the reference capacitor C_(r). Thecalibrated measurement signal 32 is provided at the non-inverting inputof operational amplifier 40, as shown. A digital word generator 31a iscoupled to a control terminal 50b of linearity DAC 50, in response towhich the voltage at an input terminal 50a thereof is multiplied by apredetermined scale factor to provide the voltage at the output terminal50c. Here again, the digital word generator 31a may comprise a pluralityof switches positioned in accordance with adjustment expression S₁ toprovide a ten bit digital input to DAC 50.

As mentioned above, the subsystem describing parameters of thetransducer 20 and signal conversion and conditioning circuit 22 aredetermined via a characterization procedure. More particularly, in theillustrative embodiment of FIG. 2, the transducer 20 has two parametersassociated therewith, each of which describes a variation thereof from anominal, predetermined value; a transducer gain parameter a=A_(p) and atransducer stray capacitance parameter b=Co₁. Likewise, the signalconversion and conditioning circuit 22 has two parameters associatedtherewith each of which describes a variation thereof from a nominal,predetermined value; a signal conversion and conditioning gain parameterc=A_(s) and a signal conversion and conditioning stray capacitanceparameter d=Co₂. If uncorrected or uncalibrated, non-unity values of thegain parameters A_(p), A_(s) would result in a gain or offset error termin the measurement signal; whereas, non-zero stray capacitanceparameters Co₁, Co₂ would result in a linearity error term.

For purposes of discussing subsystem parameter characterization, theexemplary characteristic of the object 12 to be measured is distance, ordisplacement, (i.e, such as may be further used to determined flatness)and the transducer 20 is a capacitive probe. In this capacitiveprobe/distance measuring embodiment, the probe parameters arecharacterized by positioning the probe 20 at a first, approximatedistance from the object 12, corresponding to a first probe outputsignal 27 having a first capacitance level C₁. The probe 20 issubsequently positioned at second and third positions from the object 12whose incremental distances with respect to the first position areaccurately known, resulting in output signals having second and thirdcapacitance levels C₂, C₃, respectively. The three capacitance levelvalues C₁ -C₃ and corresponding incremental distance values from thefirst probe position are used to compute the probe gain parametera=A_(p) and the probe stray capacitance parameter b=Co₁. In computingparameters a, b, intermediate parameters D_(o) and Z may first becalculated as follows: ##EQU4## where ΔD2 is the difference, ordistance, between the first and second probe positions, ΔD3 is thedifference between the first and third probe positions and ε_(o) is theconstant noted above in conjunction with equation (1). Parametersa=A_(p) and b=C_(o) may then be determined as follows: ##EQU5## where A'is the nominal, or specified active area of the probe 20, correspondingto an actual active area A.

In order to characterize the signal conversion and conditioning circuit22, the gain parameter A_(s) and the stray capacitance parameter Co₂ aredetermined. To this end, three measurements are taken, each with adifferent known capacitor value in place of the probe 20. That is, theprobe 20 is replaced by a first, and subsequently a second and a third,capacitor standard Cp₁, Cp₂, and Cp₃ corresponding measurement signalsVo₁. Vo₂, and Vo₃ respectively, are measured on signal line 32. Thethree capacitance values Cp₁, Cp₂, and Cp₃ and the correspondingmeasured signals Vo₁, Vo₂, Vo₃ are then used to compute the gainparameter c=A_(s) and the stray capacitance parameter d=Co₂ inaccordance with the following equations: ##EQU6## where Cr' is thenominal value of reference capacitor C_(r) and V_(d) ' is the nominal ACdrive voltage setting of AC source 42.

In response to the resulting gain parameters a=A_(p), c=A_(s) and thestray capacitance parameters b=Co₁, d=Co₂, such parameters aremathematically combined to provide adjustments S₁, S₂. Moreparticularly, the gain parameters A_(p), A_(s) are combined to providethe adjustment S₂ and the stray capacitance parameters Co₁, Co₂ arecombined to provide the adjustment S₁ as follows: ##EQU7## where C_(s)=Co₁ +Co₂, ρ_(a) is equal to R8R10/(R8R10+R8R6+R6R10), and ρ_(b) isequal to R6R10/(R8R10+R8R6+R6R10).

With the ten bit inputs of DACs 44, 50 thus set, the measurement systemprovides calibrated measurement signal 32. That is, each one of the DACs44, 50 corresponds to a degree of freedom of error of the measurementsystem so that when the digital word generators 31a, 31b are adjusted asdescribed above, a calibrated, error free measurement signal 32,accurately indicating the measured characteristic, is provided.Moreover, the calibration is achieved in "real time" in the sense thatonce the adjustments S₁, S₂ are provided to the system, at no timethereafter is a "uncalibrated" measurement signal provided on line 32.For example, preferably, the adjustments are provided prior toinstallation, so that the adjustable components are continuouslyadjusted upon system power up.

Referring now to FIG. 3, an alternate embodiment of the presentinvention is shown to include a virtual calibration signal processor 60.More particularly, the transducer measurement system of FIG. 3 includesa measuring circuit 62 having a transducer 64 interfacing with an object66 to provide a calibrated measurement signal 70 indicative of ameasured characteristic of the object 66. Like the measurement system ofFIG. 1, the system of FIG. 3 includes a post-processing circuit 72.Here, in addition to providing display functionality, thepost-processing circuit 72 converts a digital output signal 71 into ananalog calibrated measurement signal 74, as will be described. Thesystem of FIG. 3 operates in a somewhat like manner to the system ofFIG. 1 in that, in response to a transducer output signal P(x, a, b) online 65, a calibrated measurement signal 70 is provided. Unlike analogsignal 32 (FIG. 2) however, signal 70 is a digital calibratedmeasurement signal. The virtual characterization process described abovein conjunction with the measurement system of FIG. 1 may be used toprovide subsystem describing, or variation indicating, parameters to thesignal processor 60, as will be described. Here however, calibration isachieved by converting an analog measured signal 91 (FIG. 4) into adigital replica thereof R(F, g, h) on line 82 and the signal processor60 operates on, or processes, such digital replica signal to provide thedigital calibrated measurement signal E(R, f) on line 70. That is, thepresent embodiment does not provide adjustments S₁, S₂ for settingadjustable components 30a, 30b, respectively. Rather, the digitalreplica signal 82, or digitized version, of the measured signal 75, isprocessed to provide the digital calibrated measurement signal 70.

More particularly, measurement system of FIG. 3 includes transducer 64interfacing with object 66 to provide transducer output signal 65, withthe transducer 64 having at least one parameter, and here two parametersa, b, associated therewith and indicating variations thereof fromnominal, specified values. A signal conversion and conditioning circuit76 receives the transducer output signal 65 and includes a front endcircuit 76a for converting the transducer output signal 65 into anintermediate signal 75 having a voltage amplitude related to themeasured object characteristic. Circuit 76 further includes a signalconditioning circuit 76b for conditioning the intermediate signal 75 inthe manner noted above in conjunction with signal conditioning circuit22b (FIG. 2) and as further noted below. Here, however, signalconditioning circuit 76b additionally converts the conditionedintermediate signal 91 (FIG. 4) into a digital replica signal 82. Liketransducer 64, signal conversion and conditioning circuit 76 has atleast one, and here four, variation indicating parameters c, d, g, andh, associated therewith, as shown. The transducer parameters areprovided to the signal processor 60 in a manner described below and thedigital replica signal is provided to signal processor 60 via line 82.

Note that "virtual" is used in conjunction with signal processor 60 toindicate that component adjustments are not made to adjustablecomponents. Rather, a digitized version of the transducer output signalas processed by the front end circuit 76a and signal conditioningcircuit 76b, is processed to provide the digital calibrated measurementsignal 70.

The manner in which the measurement system of FIG. 3 achieves virtualcalibration will be better understood by referring now also to FIG. 4.Transducer 64 provides transducer output signal 65 to front end circuit76a, in response to which front end circuit 76a provides intermediatesignal 75. Front end circuit 76a may comprise the circuitry shown inFIG. 2, albeit with the exception of adjustable components 31a, 31b andDACs 44, 50. More generally, front end circuit 76a comprises circuitrysuitable for converting the transducer output signal 65 into anelectrical signal 75 having a voltage amplitude related to the measuredobject characteristic.

Signal conditioning circuit 76b receives the intermediate signal 75 andprovides the digital replica signal 82, as shown. Signal conditioningcircuit 76b includes a demodulator 90, an analog filter 92, and ananalog to digital converter 94. The demodulator 90 and filter 92comprise conventional signal conditioning circuitry, such as maycomprise the signal conditioning circuit 22b of FIGS. 1 and 2. Hereadditionally, analog to digital converter 94 is provided which, asmentioned, converts the conditioned intermediate signal 75 into adigital replica thereof 82. The digital replica signal 82 is coupled toa processor 128, such as a digital signal processor (DSP) or othersuitable processing device. Note that the virtual calibration signalprocessor 60 includes the DSP 128, as well as a digital to analogconverter 96, a lowpass filter 98, a highpass filter 100, a referencevoltage generator 102, a programmable read only memory (PROM) 104, anaddress comparator 106, an address generator 108, and a clock circuit110. Also provided is a random access memory (RAM) 112 adapted tocommunicate with a CPU 118 to facilitate calibration of the measurementsystem. Here, the clock circuit 110 provides a clock signal to addressgenerator 108, the output of which is an address provided to both thePROM 104 and the address comparator 106, as shown. Address comparator106 compares addresses received from the sync address portion 107 of DSP128 with that received by the address generator 108, in response towhich the analog to digital converter 94 is triggered. With thisarrangement, the analog to digital converter 94 is triggered in asynchronized manner with respect to preselected addresses of PROM 104corresponding to points on a digitized sinewave stored therein.

In operation, demodulator 90 demodulates the analog intermediate signal75 in accordance with a demodulation signal provided by highpass filter100, as shown. The filtered, demodulated analog output signal 91 offilter 92 is further coupled to analog to digital converter 94, thedigital replica output signal 82 of which is provided to DSP 128. Databus 122 is coupled from the RAM 112 to the DSP 128 to provide subsystemparameter data (i.e., parameters a, b, c, d, g, and h) to the DSP 128.

Considering the characterization of the subsystem parameters, transducersubsystem 64, front end subsystem 76a, and signal conditioning subsystem76b each has parameters a-b, c-d, and g-h associated therewith,respectively, describing variations thereof from nominal valuesassociated with that particular subsystem. Characterization is performedindividually on each such subsystem. Considering first the transducer64, characterization of transducer 64 is achieved in the same manner asdescribed above in conjunction with probe 20 (FIG. 2). That is, thetransducer 64 is positioned at three different distances from the object66 in accordance with which three corresponding transducer outputsignals are collected. The transducer gain parameter A and straycapacitance parameter Co₁ are then computed in accordance with equations(4)-(7) above. The front end circuit 76a is characterized in the samemanner as front end circuit 22a (FIG. 2). That is, three known capacitorstandards are used in place of the transducer 64 and measurement signalsare collected in response to each such capacitor standard. The front endgain parameter A_(s) and the front end stray capacitance parameter Co₂are then computed using equations (8) and (9) described above inconjunction with FIG. 2.

The signal conditioning circuit 76b may be characterized in terms of twoparameters; a zero offset parameter g=Z_(o) and a drive voltageparameter h=V_(d). More particularly, drive voltage parameter V_(d)refers to the actual drive voltage measured in response to a nominaldrive voltage setting V_(d) ' of reference voltage circuit 102, asconverted into a corresponding analog drive voltage by digital to analogconverter 96. The zero offset Z_(o) parameter refers to the actual drivesignal measured in response to a nominal drive voltage setting of zerovolts. In this way, the zero offset parameter is a measure of the signaloffset value introduced by the signal conditioning circuitry.

In order to characterize the signal conditioning circuit 76b, a jumper136 is positioned as shown by the dotted line in FIG. 4 and the frontend circuit 76a is removed. Stated differently, front end circuit 76a isbypassed in order to ascertain the drive voltage parameter V_(d) and thezero offset parameter Z_(o). During characterization, a desired nominaldrive voltage V_(d) ' is selected in accordance with the diameter of theprobe 64 and the range, or distance, anticipated between the transducer64 and the object 66. That is, a "look-up table" is used to select thenominal drive voltage level V_(d) '.

In operation, the above described transducer parameters a=A_(p), b=Co₁front end parameters c=A_(s), d=Co₂, and signal conditioning parametersg=V_(d), h=Z_(o), which have been stored in RAM 112, are provided to thedigital signal processor 128 via data bus 122. Signal processor 128operates on the digital replica signal 82 in accordance with the abovedetermined parameters to provide the digital calibrated measurementsignal E(R, f) on line 70. More particularly, the DSP 128 includes adigital filter 142, such as a decimating FIR filter and a digitalaveraging filter. A processor 146, or processing portion thereof,receives the characterized subsystem parameters on data bus 122 and thefiltered digital replica signal on line 148. In response to thecharacterized subsystem parameters, the processor 146 operates on, orprocesses, the filtered digital replica signal 148 to provide thedigital calibrated measurement signal E(R, f) on line 70. Moreparticularly, the processor 146 computes the digital calibratedmeasurement signal 70 in accordance with the following equation:##EQU8## where C_(s) =Co₁ +Co₂ and K₁ and K₂ are given by:

    K.sub.1 =A.sub.s (V.sub.d -Z.sub.o)=c(V.sub.d -h)          (13)

    K.sub.2 =A.sub.p ε.sub.o =aε.sub.o         (14)

The resulting digital calibrated measurement signal 70 is coupled topost processor 72, here including a digital to analog converter and alowpass filter. The output of post-processor circuit 72 is an analogversion of the digital calibrated measurement signal, or an analogcalibrated measurement signal 74, such as may be desirable for providingan analog representation of the measured characteristic.

From the above discussion of the operation of measuring circuit 62, itis apparent that the virtual calibration signal processor 60 operates toprovide calibration without actual circuit component adjustment. Thatis, the virtual calibration signal processor 60 operates on the digitalreplica signal 82 to provide a calibrated digital measurement signal 70so that the calibration is achieved digitally.

Additionally, as with the measurement system of FIGS. 1 and 2, themeasurement system of FIGS. 3 and 4 provides simplicity when replacingor adding a subsystem becomes necessary or desirable. That is, systemre-calibration is not required to replace an individual subsystem of themeasurement system. Rather, an individual subsystem, for example frontend 76a, can be replaced simply by physical replacement of the subsystemand resetting parameters c and d in RAM 112 to the new subsystemdescribing values. More specifically, once the replacement subsystem ischaracterized in the manner described above and the determined c and dparameters associated therewith provided to the RAM 112 (FIG. 4), theentire measurement system operates in a calibrated manner so that thecalibrated output signal 70 accurately indicates the measuredcharacteristic.

It is noted however, that the virtual calibration signal processor 60described above in conjunction with FIGS. 3 and 4 may be used with orwithout use of the subsystem characterization process described above.Although the calibrated measurement signals (i.e. both the digitalsignal 70 and the analog version thereof 74) may potentially be moreaccurate representations of the measured object characteristic when theabove subsystem characterization accompanies calibration by the virtualcalibration signal processor 60, the processor may nevertheless operatewith initially, or factory, determined parameters. That is, when thetransducer measurement system is manufactured, the RAM 112 may be loadedwith predetermined subsystem parameters. As long as the subsystems usedin conjunction therewith (i.e. or replacement such subsystems) areprovided with like parameters, the virtual calibration signal processor60 will maintain accurate calibration of the digital calibrationmeasurement signal 70.

It is further noted that the parameters used in conjunction with the DSP128 may be adjusted at any desired time by performing systemcalibration. That is, regardless of whether the parameters are initiallydetermined at the factory or determined in accordance with theabove-described virtual characterization procedure, such parameters maybe updated and improved by performing subsequent system calibration. Forexample, the system calibration may indicate that the parameterscurrently in use by the DSP 128 no longer provide suitably accuratemeasurement results. With the information provided by a systemcalibration, the parameters may be adjusted.

Having described the preferred embodiments of the invention, it will nowbecome apparent to one of skill in the art that other embodimentsincorporating their concepts may be used. For example, the conceptsdescribed herein are applicable to various types of measurement systemscomprising various constituent subsystems. Moreover, the apparatus andmethods described herein for achieving measurement system calibrationare equally applicable to dual channel transducer measurement systemssimply by duplicating circuitry. It is felt therefore that theseembodiments should not be limited to disclosed embodiments but rathershould be limited only by the spirit and scope of the appended claims.

We claim:
 1. A measurement system for measuring a characteristic of anobject, said system comprising:a transducer interfacing with said objectto provide a transducer output signal, said transducer having at leastone parameter indicative of a transducer transfer function associatedtherewith; a signal conversion and conditioning circuit, coupled to saidtransducer, for converting said transducer output signal into anintermediate signal having a voltage amplitude related to said objectcharacteristic and for providing a digital replica signal correspondingto said intermediate signal, said signal conversion and conditioningcircuit having at least one parameter indicative of a conversion andconditioning transfer function associated therewith; and a signalprocessor, responsive to said digital replica signal and at least oneof: the at least one transducer parameter and said transducer transferfunction, and the at least one signal conversion and conditioningparameter and said conversion and conditioning transfer function, forproviding a digital calibrated measurement signal indicative of saidmeasured object characteristic.
 2. The measuring circuit recited inclaim 1 wherein said signal processor adjusts said digital replicasignal in accordance with a mathematical combination of said at leastone transducer parameter and said at least one signal conversion andconditioning parameter to provide said digital calibrated measurementsignal.
 3. The measurement system recited in claim 2 wherein said signalconversion and conditioning circuit includes a front end circuit forconverting said transducer output signal into said intermediate signaland a signal conditioning circuit for conditioning said intermediatesignal and providing said digital replica signal.
 4. The measurementsystem recited in claim 3 further comprising means for bypassing saidfront end circuit to determine said at least one signal conversion andconditioning parameter.
 5. The measurement system recited in claim 2further comprising a memory device for storing said at least onetransducer parameter and said at least one signal conversion andconditioning parameter for use by said signal processor.
 6. Themeasurement system recited in claim 2 wherein said signal processorincludes a digital signal processor.
 7. The measurement system recitedin claim 2 further comprising means for converting said digitalcalibrated measurement signal into an analog calibrated measurementsignal.
 8. A method for measuring a characteristic of an object,comprising the steps of:measuring at least one parameter indicative of atransducer transfer function of a transducer to provide a transducerparameter value, said transducer being adapted for interfacing with saidobject to provide a transducer output signal; measuring at least oneparameter indicative of a signal conversion and conditioning transferfunction of a signal conversion and conditioning circuit, said signalconversion and conditioning circuit coupled to said transducer, forconverting said transducer output signal into an intermediate signalhaving a voltage amplitude related to said measured objectcharacteristic and providing a digital replica signal corresponding tosaid intermediate signal; and processing said digital replica signalwith a signal processor by processing said digital replica signal inaccordance with at least one of: the at least one transducer parameterand said transducer transfer function, and the at least one signalconversion and conditioning parameter and said conversion andconditioning transfer function to provide a digital calibratedmeasurement signal indicative of said measured object characteristic. 9.The method recited in claim 8 wherein said digital replica signalprocessing step includes the step of mathematically combining said atleast one transducer parameter and said at least one signal conversionand conditioning parameter.
 10. The measuring circuit recited in claim 8further comprising the step of converting said digital calibratedmeasurement signal into an analog calibrated measurement signal.